Mixed Topic Worksheet Grades 6/7: Day 039
- 1
Question 1. The table shows the ages of 10 members of a club. Work out an estimate for the mean age.
Mean, Mode & Median from a Grouped Frequency Table▶ Show worked answerHide worked answer
- M1: 5 × 3 + 15 × 5 + 25 × 2
- M1: divides the total of the products by 10
- A1: 14 years
Answer: 14 years[3 marks] - 2
Question 2. f(x) = 3x² - 4
g(x) = 20 - x²
Which is larger, f(3) or g(-3)?
You must show your working.Fundamentals of Functions▶ Show worked answerHide worked answer
- M1: 3 × 3² - 4
- M1: 20 - (-3)²
- A1: f(3) = 23 is larger than g(-3) = 11
Answer: f(3)[3 marks] - 3
Question 3. A shape is reflected in the line y = -x.
Which of the points (2, -2), (2, 2) and (-1, -1) is invariant?
Give a reason for your answer.Invariant Points▶ Show worked answerHide worked answer
- M1: (2, 2) maps to (-2, -2) and (-1, -1) maps to (1, 1)
- A1: (2, -2)
- B1: it lies on the mirror line y = -x
Answer: (2, -2), because it lies on the line y = -x[3 marks] - 4
Question 4. Triangle ABC is isosceles.
AB = AC = 10 cm
Angle BAC = 150^°
sin 150^° = 1/2
Work out the area of triangle ABC. You must not use a calculator.Using the Area Rule with Isosceles Triangles▶ Show worked answerHide worked answer
- M1: 1/2 × 10 × 10 × 1/2
- A1: 25
Answer: 25 cm²[2 marks] - 5
Question 5. Here is a speed-time graph for a bus journey.
(a) Work out the total distance travelled. [3]
(b) Work out the average speed for the whole journey. [2]Calculating Total Distance Travelled Using Speed-Time Graphs▶ Show worked answerHide worked answer
- (a) M2: ½ × 10 × 10 = 50 for each end section, 10 × (40 - 10) = 300
- (a) A1: 50 + 300 + 50 = 400 m
- (b) M1: 400 ÷ 50
- (b) A1: 8 m/s
Answer: (a) 400 m; (b) 8 m/s[5 marks]
Mixed Topic Worksheet Grades 6/7: Day 039
- 1
Question 1. The table shows the ages of 10 members of a club. Work out an estimate for the mean age.
[3 marks]Mean, Mode & Median from a Grouped Frequency Table▶ Show worked answerHide worked answer
- M1: 5 × 3 + 15 × 5 + 25 × 2
- M1: divides the total of the products by 10
- A1: 14 years
Answer: 14 years - 2
Question 2. f(x) = 3x² - 4
[3 marks]
g(x) = 20 - x²
Which is larger, f(3) or g(-3)?
You must show your working.Fundamentals of Functions▶ Show worked answerHide worked answer
- M1: 3 × 3² - 4
- M1: 20 - (-3)²
- A1: f(3) = 23 is larger than g(-3) = 11
Answer: f(3) - 3
Question 3. A shape is reflected in the line y = -x.
[3 marks]
Which of the points (2, -2), (2, 2) and (-1, -1) is invariant?
Give a reason for your answer.Invariant Points▶ Show worked answerHide worked answer
- M1: (2, 2) maps to (-2, -2) and (-1, -1) maps to (1, 1)
- A1: (2, -2)
- B1: it lies on the mirror line y = -x
Answer: (2, -2), because it lies on the line y = -x - 4
Question 4. Triangle ABC is isosceles.
[2 marks]
AB = AC = 10 cm
Angle BAC = 150^°
sin 150^° = 1/2
Work out the area of triangle ABC. You must not use a calculator.Using the Area Rule with Isosceles Triangles▶ Show worked answerHide worked answer
- M1: 1/2 × 10 × 10 × 1/2
- A1: 25
Answer: 25 cm² - 5
Question 5. Here is a speed-time graph for a bus journey.
[5 marks]
(a) Work out the total distance travelled. [3]
(b) Work out the average speed for the whole journey. [2]Calculating Total Distance Travelled Using Speed-Time Graphs▶ Show worked answerHide worked answer
- (a) M2: ½ × 10 × 10 = 50 for each end section, 10 × (40 - 10) = 300
- (a) A1: 50 + 300 + 50 = 400 m
- (b) M1: 400 ÷ 50
- (b) A1: 8 m/s
Answer: (a) 400 m; (b) 8 m/s
Mixed Topic Worksheet Grades 6/7: Day 039
- 1
Question 1. The table shows the ages of 10 members of a club. Work out an estimate for the mean age.
Mean, Mode & Median from a Grouped Frequency Table▶ Show worked answerHide worked answer
- M1: 5 × 3 + 15 × 5 + 25 × 2
- M1: divides the total of the products by 10
- A1: 14 years
Answer: 14 years[3 marks] - 2
Question 2. f(x) = 3x² - 4
g(x) = 20 - x²
Which is larger, f(3) or g(-3)?
You must show your working.Fundamentals of Functions▶ Show worked answerHide worked answer
- M1: 3 × 3² - 4
- M1: 20 - (-3)²
- A1: f(3) = 23 is larger than g(-3) = 11
Answer: f(3)[3 marks] - 3
Question 3. A shape is reflected in the line y = -x.
Which of the points (2, -2), (2, 2) and (-1, -1) is invariant?
Give a reason for your answer.Invariant Points▶ Show worked answerHide worked answer
- M1: (2, 2) maps to (-2, -2) and (-1, -1) maps to (1, 1)
- A1: (2, -2)
- B1: it lies on the mirror line y = -x
Answer: (2, -2), because it lies on the line y = -x[3 marks] - 4
Question 4. Triangle ABC is isosceles.
AB = AC = 10 cm
Angle BAC = 150^°
sin 150^° = 1/2
Work out the area of triangle ABC. You must not use a calculator.Using the Area Rule with Isosceles Triangles▶ Show worked answerHide worked answer
- M1: 1/2 × 10 × 10 × 1/2
- A1: 25
Answer: 25 cm²[2 marks] - 5
Question 5. Here is a speed-time graph for a bus journey.
(a) Work out the total distance travelled. [3]
(b) Work out the average speed for the whole journey. [2]Calculating Total Distance Travelled Using Speed-Time Graphs▶ Show worked answerHide worked answer
- (a) M2: ½ × 10 × 10 = 50 for each end section, 10 × (40 - 10) = 300
- (a) A1: 50 + 300 + 50 = 400 m
- (b) M1: 400 ÷ 50
- (b) A1: 8 m/s
Answer: (a) 400 m; (b) 8 m/s[5 marks]